L.,
I understand that you are concerned about your child and like all parents want the best for them. but i can honestly say that i sucked my thumb well into my teenage years. and the harder people tried to make me stop the more determined i was to keep doing it. fact of the matter is to me thumb sucking was a way for me to feel comfortable and secure. it was soothing for me well into my teenage years. as a child i was able to comfort myself when i felt i needed it and even now when i am sleepng my husband sometimes catches me sucking my thumb. let her do her thing. if this is what she needs to feel comfort than it shouldn't be such an issue. eventually my mother introduced a blanky to me. she always made sure that it had something silky around the edges that i could rub that helped me in quitting thumbsucking. it became another way of self soothing. and i still am drawn to things that have silky stuff on it. i think personally thumbsucking is ok. it didn't affect me and it didn't stunt my growth in any form (personality, mentally, or any other form). of course its up to you as parent but i would suggest that you let her self soothe or maybe try something like a blanky or special stuffed animal instead if thats what she feels she needs to have with her.
as for her thumb being chapped and cracking if you are comfortable with it let her know she has two thumbs and while one is healing she can suck the other. try putting bag balm on her thumb and wrap it up overnight or during the day and continue this until it heals. bag balm is used on cows utters so they don't get chapped. i have used it for years and i swear by it of course its not something i would suggest she put in her mouth but if you wrap her thumb well enough you shouldnt worry it just need to soak in more than anything. otherwise aloe can be useful but its not always great for chapped skin. if youare still uncomfortable with it find a moisturizing hand soap and constantly wash her hands. i know that my thumb was always chapped when i was a kid because of it. of course i also grew up in cold weather so thats one thing you have going for you. good luck.